Introduction
Hi, I am quite sure I made an ignorant misinterpertation. Hence, I will apologize in advance.
The question is about the paper AAM Revisited in respect to equation 30 of section 4.1.2. In it, each (factor of the)Jacobian(delta W/delta x and y) is computed as (1-a-b, 0) and (0, 1-a-b) where a and b are given by equation 25 and 26 in section 4.1.1.
Also, the jacobian is evaluated in respect to vertex xi, assuming there is no alternation to the mesh(given in the paper in page 34 figure 13, precomputation step 4 in which the author states that the jacobians are evaluated in respect to (x;0) where the 0 portion is the variation).
Essentially the xio and xi in equation 25 and 26 should be equivalent as well as yio and yi which is written in the paper as p = 0 as well as q = 0.
Question
Here, I will get to my question. If xi and xio as well as yi and yio are equivalent when computing the factor of a jacobian given in equation 30, given the fact that in such situation a and b will evaluate to 0(as the numerator will become 0) as is evident from equation 25 and 26, shouldn't the values in equation 30 always be (1,0) and (0,1)? Thanks in advance!
Note
As I have not seen any other research paper related questions in stackoverflow(possibly due to my lack of experience), I suspect that this kind of question is best asked on a different site. If that is the case, may I ask any recommandations?